Recent experiments have demonstrated that the regime of very few electrons in quantum dots (QDs) displays peculiar properties, different from the many-electron case, both in transport [1] and light scattering [2] spectroscopies. However, no direct observation of such effects in wave function (WF) images was obtained so far. Among the available techniques, scanning tunneling spectroscopy (STS) provides spectacular images of dot WFs [3]. Experiments so far have shown maps of localized orbitals, that could be explained in terms of an independent-electron model.
Here we focus on QDs where we expect that electron-electron interaction may instead be relevant. We show that the WF actually probed by STS is the space-resolved spectral density amplitude of the one-particle propagator (or quasi-particle wave function), which can considerably deviate from the independent-electron WF, due to correlation effects [4]. To this aim we investigate, both experimentally and theoretically, STS WF maps of single and freestanding strain-induced InAs QDs grown on GaAs(001). The sequence of measured WFs cannot be explained in terms of single-electron orbitals. We compare the measured maps with those predicted by a numerical model which takes into account QD anisotropy and the full correlation effects, and we are able to separately identify ground- and excited-state WFs corresponding to the injection of a first and a second electron into the QD. This interpretation is supported by the analysis of the measured differential conductance as a function of the stabilization current.
The quasi-particle WF corresponding to the ground state → ground state tunneling process N = 1 → N = 2 displays a surprising two-peak charge modulation which is inconsistent with the simple picture of a doubly occupied s-like orbital.This effect, qualitatively reproduced by our simulations, is due to the destructive interference between different components of the correlated singlet wave function.
[1] M. Avinum-Kalish et al., Nature 436, 529 (2005).
[2] C. P. Garcia et al., PRL 95, 266806 (2005).
[3] T. Maltezopoulos et al., PRL 91, 196804 (2003).
[4] M. Rontani et al., PRB 71, 233106 (2005). |